Abstract paintings, unlike representational paintings, have designs, shapes and colors that do not look like specific physical objects. They are more difficult to analyze than representational paintings because you may have no idea what you are looking at. Artists in the early 20th century began painting in this manner as a way of evoking deep unconscious emotions. By experiencing and thinking about your emotions, you can analyze an abstract painting.
Observe the painting for at least ten minutes without letting yourself be distracted. Pay attention to how the painting makes you feel and how your emotions change from when you first looked at the painting to after you have spent some time with it. Abstract painters use art as a tool for indirect access to their viewers' inner psyches. Relax and allow the art to have an impact on yours.
Concentrate on the specific content and technique of the painting. Make note of how the painter uses color, lines, textures and balance. Observe how different elements are distributed across the canvas. Decide how you would describe the painting to someone who couldn't see it.
Research the artist's biography either using the internet resources below, by going to a library and asking a librarian or by looking in a book on art in the reference section. Find out how your painting compares to the artist's earlier and later works. Discover what was happening in the artist's life at the time she produced the painting.
Research how your painting fits with the course of art history. Find out what paintings it reacted to and what paintings reacted to it. See what other kinds of paintings were being produced at that time. Investigate what art critics have had to say about the painting and see if it has been copied and by whom.
Return to the painting and look at it again. Keeping in mind what you now know about the painting, ask yourself how the painting now makes you feel. Consider how your emotions are influenced by your research on the artist and on the painting's place in history.